A storage device, such as a magnetic disc drive, stores data on a recording medium that is divided into a large number of tracks. The data are stored and retrieved by a head that is positioned over a desired track by a servo system. This positioning is typically performed using servo fields located on the medium. As the head passes over the servo fields, it generates a servo signal that identifies the location of the head. Based on this location, the servo system adjusts the head's position so that it moves toward the desired position.
Preferably, the signals from the servo fields can be combined to provide a linear position error signal. If the position error signal is linear, a change in the position error signal corresponds to an equal amount of change in the position of the head. This allows the servo system to move the head directly from the position error signal. If the position error signal is not linear, the servo system must perform further calculations to determine the position from the position error signal. In some devices, these additional calculations are avoided by treating a non-linear position error signal as a linear signal. However, using such linear estimations reduces the accuracy of the servo positioning.
Typically, the position error signal is created from a series of position error values that are based upon a normal position error value, N, and/or a quadrature position error value, Q. Both values change in a cyclical manner as the head moves radially along the disc. If these changes are graphed as a function of radial position, they have the appearance of cyclical signals, which in the art are known as the normal position error signal and the quadrature position error signal. The quadrature signal has the same cyclical pattern as the normal signal, except that it is ninety degrees out of phase from the normal signal. Thus, at a radial location where the normal signal is at a maximum the quadrature signal is at zero. Similarly, at a different radial location where the quadrature signal is at a maximum, the normal signal is at zero.
The normal and quadrature signals developed in the prior art have had limited linear ranges. Because of this, the art has attempted to extend their linear range. One such extension produces a normal position error signal NPQ, and a quadrature position error signal NMQ. An NPQ signal is produced by adding an N and a Q position error signal together. An NMQ position error signal is created by subtracting a Q position error signal from an N position error signal. To produce a complete position error signal, the servo system commutates between the NPQ and the NMQ signals at commutation points or boundaries.
For narrow width heads, the NMQ and NPQ signals are more linear about their respective zeros than the N and Q signals. However, the complete position error signal produced by the NPQ and NMQ signals tends to include discontinuities created at the commutation boundaries. These discontinuities are generated by differences in the magnitudes of the NPQ and NMQ signals. Such discontinuities in the position error signal result in decreased track following accuracy.
To remove the discontinuities at the commutation boundaries, the art developed a second extended linearization for position error signals, known as "SEAMLESS". The normal and quadrature SEAMLESS signals are described by the formulas: ##EQU1##
where SEAMLESS.sub.n is the normal SEAMLESS signal, SEAMLESS.sub.q is the quadrature SEAMLESS signal, which is ninety degrees out of phase from SEAMLESS.sub.n, and .vertline.N.vertline. and .vertline.Q.vertline. are the magnitudes of N and Q, respectively.
The seamless formulas normalize the normal and quadrature signals to +/-1. In addition, for wider heads, the resulting normal and quadrature SEAMLESS traces will be very linear between +/-1. Unfortunately, for typical heads with narrow magnetic reader widths, SEAMLESS actually increases cross-track non-linearity.
Thus, the prior art fails to provide a sufficiently linear position error signal for narrow heads that does not include discontinuities. The present invention addresses this and other problems, and offers other advantages over the prior art.